# KdV hierarchies and quantum Novikov's equations

@inproceedings{Buchstaber2021KdVHA, title={KdV hierarchies and quantum Novikov's equations}, author={V M Buchstaber and Alexandre V. Mikhailov}, year={2021} }

The paper begins with a review of the well known Novikov equations and corresponding finite KdV hierarchies. For any positive integer N we give an explicit description of the N-th Novikov equation and its first integrals. Its finite KdV hierarchy consists of N compatible integrable polynomial dynamical systems in C . Then we discuss a non-commutative version of the N-th Novikov equation defined on a finitely generated free associative algebra BN with 2N generators. In BN , for N = 1, 2, 3, 4…

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